Question

The value of ${\sin }^{-1}\left(\frac{1}{2}\right)+{\sec }^{-1}\left(\frac{1}{2}\right)$ is

[1 mark]

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. not defined

Answer 1

The correct option is D not defined

${\sin }^{-1}\left(\frac{1}{2}\right)+{\sec }^{-1}\left(\frac{1}{2}\right)$
Domain of ${\sec }^{-1}x$ is $(-\infty ,-1]\cup [1,\infty )$
and $\frac{1}{2}\notin (-\infty ,-1]\cup [1,\infty )$
$\therefore {\sec }^{-1}\left(\frac{1}{2}\right)$ is not defined.